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The PRIDE Lab at GNSS Research Center of Wuhan University has developed an open-source software for GPS precise point positioning ambiguity resolution (PPP-AR) (i.e., PRIDE PPP-AR). Released under the terms of the GNU General Public License version 3 (GPLv3, http://www.gnu.org/licenses/gpl.html), PRIDE PPP-AR supports relevant research, application and development with GPS post-processing PPP-AR. PRIDE PPP-AR is mainly composed of two modules, undifferenced GPS processing and single-station ambiguity resolution. Undifferenced GPS processing provides float solutions with wide-lane and narrow-lane ambiguity estimates. Later, single-station ambiguity resolution makes use of the phase clock/bias products, which are released also by the PRIDE Lab at ftp://pridelab.whu.edu.cn/pub/whu/phasebias/, to recover the integer nature of single-station ambiguities and then carry out integer ambiguity resolution. PRIDE PPP-AR is based on a least-squares estimator to produce daily, sub-daily or kinematic solutions for various geophysical applications. To facilitate the usage of this software, a few user-friendly shell scripts for batch processing have also been provided along with PRIDE PPP-AR. In this article, we use 1 month of GPS data (days 001–031 in 2018) to demonstrate the performance of PRIDE PPP-AR software. The PRIDE Lab is committed to consistently improve the software package and keep users updated through our website.

A bstract Recently, Ciambelli, Leigh, and Pai (CLP) [ arXiv:2111.13181 ] have shown that nonzero charges integrating Hamilton’s equation can be defined for all diffeomorphisms acting near the boundary of a subregion in a gravitational theory. This is done by extending the phase space to include a set of embedding fields that parameterize the location of the boundary. Because their construction differs from previous works on extended phase spaces by a covariant phase space ambiguity, the question arises as to whether the resulting charges are unambiguously defined. Here, we demonstrate that ambiguity-free charges can be obtained by appealing to the variational principle for the subregion, following recent developments on dealing with boundaries in the covariant phase space. Resolving the ambiguity produces corrections to the diffeomorphism charges, and also generates additional obstructions to integrability of Hamilton’s equation. We emphasize the fact that the CLP extended phase space produces nonzero diffeomorphism charges distinguishes it from previous constructions in which diffeomorphisms are pure gauge, since the embedding fields can always be eliminated from the latter by a choice of unitary gauge. Finally, we show that Wald-Zoupas charges, with their characteristic obstruction to integrability, are associated with a modified transformation in the extended phase space, clarifying the reason behind integrability of Hamilton’s equation for standard diffeomorphisms.

Precise ionospheric information, as like precise satellite orbits, clocks, and code/phase biases, is a critical factor for achieving fast integer ambiguity resolution in precise point positioning (PPP-AR). This study develops an ionosphere-weighted (IW) undifferenced and uncombined PPP real-time kinematic (PPP-RTK) network model using code and phase observations. We introduce between-station single-differenced ionospheric delay pseudo-observations to take advantage of the similar characteristics of ionospheric delays between two receivers tracking the same satellite. The estimable ionospheric parameters are commonly affected by the differential code bias referring to a particular receiver assigned as pivot, which facilitates the ionospheric interpolation at the user side. Then, the kinematic positioning performance of the IW PPP-RTK user model is analyzed and compared with those of PPP-AR without ionospheric corrections, RTK, and IW-RTK models during low and high solar activity days. The results show that for the PPP-RTK model, the positioning errors converge to thresholds of 2 cm for the horizontal components and 5 cm for the vertical component within 20 epochs, and the positioning errors become stable after an initialization of 20 epochs with root-mean-squared (RMS) values of approximately 0.47, 0.58 and 1.66 cm for the east, north and up components, respectively, which are superior to those of the other three models. Owing to the high ionospheric disturbance influence, the RMS values of the east and up components increase by approximately double and the mean time-to-first-fix increases by 61.5% for the PPP-RTK case.

Factor graph optimization has been widely used for state estimation in robotic SLAM community. Extensive algorithms have been proposed for camera/LiDAR/INS based SLAM. However, GNSS positioning based on factor graph optimization is limited, which prevents the introduction of high precise GNSS to robotic SLAM community. The current implementations are focused on pseudorange or RTK based positioning. PPP with ambiguity resolution (AR) is the state-of-the-art positioning technique for the past decade. Therefore, the PPP AR based on factor graph optimization is proposed, in which the pseudorange and carrier phases factors are constructed from the error equations of raw observations, while the ambiguity resolution factor is built from the ambiguity resolution. Results from 80 MGEX stations show that the average accuracy of static PPP is improved from 1.25, 0.61 and 2.29 cm to 0.81, 0.5 and 2.1 cm, corresponding to improvements of 35.1%, 18.7% and 8.7% in east, north, and up directions, respectively. As for kinematic PPP, the average accuracy is improved from 2.62, 2.21 and 5.8 cm to 1.64, 1.74 and 5.37 cm, corresponding to improvements of 37.5%, 21.6% and 7.4% in east, north, and up directions, respectively. The kinematic PPP was also verified with real-world data collected from a moving vehicle. After the first ambiguity fixing, the accuracy of PPP is improved from 3.7, 2.1 and 10.1 cm to 1.6, 2.0 and 9.0 cm for east, north and up component, respectively, corresponding to improvements of 32%, 5% and 11%. The above results confirm the efficiency of the proposed algorithm.

The accuracy of navigation information is essential for modern transport systems. Such information includes position, velocity and attitude. Because of the physical characteristics of the operational environments, integration of GNSS with inertial measurement units (IMU) is commonly used. However, conventional integrated algorithms suffer from low-quality GNSS measurements due to either inaccurate pseudoranges or difficulty of ambiguity resolution when using carrier phase measurements in urban environments. We propose a Time-Difference-Carrier-Phase (TDCP) derivation controlled GNSS/IMU integration scheme. The proposed algorithm enables a TDCP-based control vector construction, including relative position, velocity, heading and pitch, which makes it possible to obtain accurate changes in position, namely delta position, altitude and velocity estimations. These estimated changes are then used to feed a loosely coupled GNSS/IMU integration system. Real-world test results show that the proposed integrated navigation scheme is superior to the conventional algorithm, with accuracy improvements of more than 38% in 3D positioning, 30% in 3D velocity, 35% in roll, 44% in pitch and 39% in heading.

This paper presents the reconstruction of missing transverse momentum ( pTmiss ) in proton–proton collisions, at a center-of-mass energy of 13 TeV. This is a challenging task involving many detector inputs, combining fully calibrated electrons, muons, photons, hadronically decaying τ -leptons, hadronic jets, and soft activity from remaining tracks. Possible double counting of momentum is avoided by applying a signal ambiguity resolution procedure which rejects detector inputs that have already been used. Several pTmiss ‘working points’ are defined with varying stringency of selections, the tightest improving the resolution at high pile-up by up to 39% compared to the loosest. The pTmiss performance is evaluated using data and Monte Carlo simulation, with an emphasis on understanding the impact of pile-up, primarily using events consistent with leptonic Z decays. The studies use 140fb-1 of data, collected by the ATLAS experiment at the Large Hadron Collider between 2015 and 2018. The results demonstrate that pTmiss reconstruction, and its associated significance, are well understood and reliably modelled by simulation. Finally, the systematic uncertainties on the soft pTmiss component are calculated. After various improvements the scale and resolution uncertainties are reduced by up to 76% and 51% , respectively, compared to the previous calculation at a lower luminosity.

Along with the rapid development of GNSS, not only BeiDou, but also Galileo, and the newly launched GPS satellites can provide signals on three frequencies at present. To fully take advantage of the multi-frequency multi-system GNSS observations on precise point positioning (PPP) technology, this study aims to implement the triple-frequency ambiguity resolution (AR) for GPS, Galileo, and BeiDou-2 combined PPP using the raw observation model. The processing of inter-frequency clock bias (IFCB) estimation and correction in the context of triple-frequency PPP AR has been addressed, with which the triple-frequency uncalibrated phase delay (UPD) estimation is realized for real GPS observations for the first time. In addition, the GPS extra-wide-line UPD quality is significantly improved with the IFCB correction. Because of not being contaminated by the IFCB, the raw UPD estimation method is directly employed for Galileo which currently has 24 satellites in operation. An interesting phenomenon is found that all Galileo satellites except E24 have a zero extra-wide-lane UPD value. With the multi-GNSS observations provided by MGEX covering 15 days, the positioning solutions of GPS + Galileo + BeiDou triple-frequency PPP AR have been conducted and analyzed. The triple-frequency kinematic GNSS PPP AR can achieve an averaged 3D positioning error of 2.2 cm, and an averaged convergence time of 10.8 min. The average convergence time can be reduced by triple-frequency GNSS PPP AR by 15.6% compared with dual-frequency GNSS PPP AR, respectively. However, the additional third frequency has only a marginal contribution to positioning accuracy after convergence.

This paper describes experiments showing that some tasks in natural language processing (NLP) can already be performed using quantum computers, though so far only with small datasets. We demonstrate various approaches to topic classification. The first uses an explicit word-based approach, in which word-topic weights are implemented as fractional rotations of individual qubits, and a phrase is classified based on the accumulation of these weights onto a scoring qubit, using entangling quantum gates. This is compared with more scalable quantum encodings of word embedding vectors, which are used to compute kernel values in a quantum support vector machine: this approach achieved an average of 62% accuracy on classification tasks involving over 10000 words, which is the largest such quantum computing experiment to date. We describe a quantum probability approach to bigram modeling that can be applied to understand sequences of words and formal concepts, investigate a generative approximation to these distributions using a quantum circuit Born machine, and introduce an approach to ambiguity resolution in verb-noun composition using single-qubit rotations for simple nouns and 2-qubit entangling gates for simple verbs. The smaller systems presented have been run successfully on physical quantum computers, and the larger ones have been simulated. We show that statistically meaningful results can be obtained, but the quality of individual results varies much more using real datasets than using artificial language examples from previous quantum NLP research. Related NLP research is compared, partly with respect to contemporary challenges including informal language, fluency, and truthfulness.

Precise point positioning (PPP) can be significantly improved with the multi- multi-GNSS constellation, but it still takes more than 10 min to obtain positioning results at centimeter-level accuracy. We develop a multi-constellation (GPS + GLONASS + Galileo + BDS) PPP ambiguity resolution (AR) method augmented by precise atmospheric corrections to achieve instantaneous centimeter-level positioning. In the proposed method, multi-constellation PPP fixed solutions are carried out at the reference network. The precise tropospheric delays are derived from the ionospheric-free (IF) phase observations while the slant ionospheric delays are extracted from the raw phase observations after the ambiguities are fixed. Afterward, they are provided to user stations for correcting the raw observations. Using these precise atmospheric corrections, one can achieve an instantaneous ambiguity resolution (IAR) with an accuracy of several centimeters. This method is validated experimentally with the Australian Regional GPS Network (ARGN), the South Pacific Regional GNSS Network (SPRGN) and the Hong Kong CORS. The ambiguity resolution can be achieved in several seconds with regionally computed atmospheric corrections, and the convergence time of positioning is significantly shortened compared to the PPP float and PPP-AR solution. Besides, the regional augmentation PPP (RA-PPP) also provides an advantage over network real-time kinematic (NRTK); the time to first ambiguity resolution can be shortened from 3 epochs to 1 epoch. The results also demonstrate the contribution of multi-constellation fusion to the PPP IAR in terms of positioning accuracy and reliability. The percentage of IAR can be up to 90.0% for multi-GNSS solutions, while the percentage for GPS-only solution is 7.2% when the cutoff elevation angle is 40°.

Bridge deformation monitoring requires high-precision and reliable positioning to ensure structural safety, but achieving this remains a challenge due to signal obstructions and unmodeled errors in the Global Navigation Satellite System (GNSS). This study proposes a GNSS millimeter-level deformation monitoring system that integrates adaptive innovation, posterior residuals, robust estimation, the least-squares ambiguity decorrelation adjustment method, and the partial ambiguity resolution method to enhance positioning accuracy and reliability. To further mitigate positioning errors, a multi-stage filtering strategy based on median filtering and mean filtering is applied to refine the fixed solutions. This proposed method was validated using two datasets from the bridge monitoring, and positioning results demonstrate that the proposed method achieves significant improvements in both ambiguity fixed rates and positioning accuracy, with three-dimensional accuracy enhancements of 73.5% and 71.2% over traditional methods for the two datasets, respectively. Multi-stage filtering effectively smooths and stabilizes positioning results by mitigating outliers and noise, achieving millimeter-level precision with standard deviations of 4.3 mm, 1.0 mm, and 7.4 mm in the east, north, and up directions for one dataset, and 2.6 mm, 0.9 mm, and 4.2 mm for the other. The findings highlight the potential of integrating reliable ambiguity resolution with multi-stage filtering for GNSS monitoring systems, addressing critical challenges in achieving real-time millimeter-level deformation detection.